Evaluate The Expression:a. $\sqrt{25}(\sqrt[15]{5}+\sqrt[3]{62}$\] B. $\sqrt{28} \times \sqrt[3]{15} + (\sqrt{26} \times \sqrt{20}$\]
Introduction
Mathematical expressions are a fundamental part of mathematics, and evaluating them is a crucial skill that every student should possess. In this article, we will evaluate two mathematical expressions: a. and b. . We will break down each expression, simplify it, and provide the final answer.
Expression a:
Simplifying the Square Root
The first step in evaluating expression a is to simplify the square root of 25. We know that the square root of 25 is 5, since 5 multiplied by 5 equals 25.
\sqrt{25} = 5
Simplifying the Cube Root
Next, we need to simplify the cube root of 62. However, we cannot simplify it further, so we will leave it as is.
\sqrt[3]{62} = \sqrt[3]{62}
Simplifying the 15th Root
Now, we need to simplify the 15th root of 5. However, we cannot simplify it further, so we will leave it as is.
\sqrt[15]{5} = \sqrt[15]{5}
Combining the Terms
Now that we have simplified each term, we can combine them using the distributive property.
5(\sqrt[15]{5}+\sqrt[3]{62}) = 5\sqrt[15]{5} + 5\sqrt[3]{62}
Evaluating the Expression
To evaluate the expression, we need to calculate the value of each term.
5\sqrt[15]{5} = 5 \times 5^{1/15} = 5^{16/15}
5\sqrt[3]{62} = 5 \times \sqrt[3]{62} = 5 \times 3.974 = 19.87
Final Answer
The final answer for expression a is:
5^{16/15} + 19.87
Expression b:
Simplifying the Square Root
The first step in evaluating expression b is to simplify the square root of 28. We know that the square root of 28 is √(4*7) = 2√7.
\sqrt{28} = 2\sqrt{7}
Simplifying the Cube Root
Next, we need to simplify the cube root of 15. However, we cannot simplify it further, so we will leave it as is.
\sqrt[3]{15} = \sqrt[3]{15}
Simplifying the Product of Square Roots
Now, we need to simplify the product of the square roots of 26 and 20. We know that the square root of 26 is √(413) = 2√13 and the square root of 20 is √(45) = 2√5.
\sqrt{26} \times \sqrt{20} = 2\sqrt{13} \times 2\sqrt{5} = 4\sqrt{65}
Combining the Terms
Now that we have simplified each term, we can combine them using the distributive property.
2\sqrt{7} \times \sqrt[3]{15} + 4\sqrt{65} = 2\sqrt{7} \times \sqrt[3]{15} + 4\sqrt{65}
Evaluating the Expression
To evaluate the expression, we need to calculate the value of each term.
2\sqrt{7} \times \sqrt[3]{15} = 2 \times \sqrt{7} \times 2.154 = 8.62
4\sqrt{65} = 4 \times \sqrt{65} = 4 \times 8.06 = 32.24
Final Answer
The final answer for expression b is:
8.62 + 32.24
Conclusion
Introduction
Evaluating mathematical expressions is a crucial skill that every student should possess. In our previous article, we evaluated two mathematical expressions: a. and b. . In this article, we will provide a Q&A guide to help you better understand how to evaluate mathematical expressions.
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify square roots?
A: To simplify a square root, we need to find the largest perfect square that divides the number inside the square root. For example, to simplify √(36), we can write it as √(6*6) = 6√6.
Q: How do I simplify cube roots?
A: To simplify a cube root, we need to find the largest perfect cube that divides the number inside the cube root. For example, to simplify ∛(64), we can write it as ∛(444) = 4∛4.
Q: What is the difference between a rational and irrational number?
A: A rational number is a number that can be expressed as the ratio of two integers, i.e., a/b, where a and b are integers and b is not zero. An irrational number is a number that cannot be expressed as the ratio of two integers.
Q: How do I evaluate an expression with multiple terms?
A: To evaluate an expression with multiple terms, we need to follow the order of operations. We need to evaluate any parentheses first, then any exponents, then any multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right.
Q: What is the difference between a variable and a constant?
A: A variable is a symbol that represents a value that can change. A constant is a value that does not change.
Q: How do I simplify an expression with variables?
A: To simplify an expression with variables, we need to follow the order of operations. We need to evaluate any parentheses first, then any exponents, then any multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right.
Q: What is the difference between a linear and quadratic expression?
A: A linear expression is an expression that can be written in the form ax + b, where a and b are constants and x is a variable. A quadratic expression is an expression that can be written in the form ax^2 + bx + c, where a, b, and c are constants and x is a variable.
Conclusion
Evaluating mathematical expressions is a crucial skill that every student should possess. In this article, we provided a Q&A guide to help you better understand how to evaluate mathematical expressions. We hope that this article has provided you with a better understanding of how to evaluate mathematical expressions.
Common Mistakes to Avoid
- Not following the order of operations
- Not simplifying expressions before evaluating them
- Not using parentheses to group terms correctly
- Not evaluating expressions with variables correctly
- Not simplifying expressions with multiple terms correctly
Tips for Evaluating Mathematical Expressions
- Read the expression carefully and identify any parentheses, exponents, multiplication and division operations, and addition and subtraction operations.
- Follow the order of operations to evaluate the expression.
- Simplify expressions before evaluating them.
- Use parentheses to group terms correctly.
- Evaluate expressions with variables correctly.
- Simplify expressions with multiple terms correctly.
By following these tips and avoiding common mistakes, you can become proficient in evaluating mathematical expressions and solve problems with confidence.